Question 1

A portfolio consists of 800 shares of stock and 100 calls on that stock. If the hedge ratio for the call is 0.5, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

−$800 + [−$100(0.5)] = −$850.

Question 2

If the hedge ratio for a stock call is 0.30, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

Call hedge ratio = N(d1); Put hedge ratio = N(d1) − 1; 0.3 − 1.0 = −0.7.

Question 3

A put option on the S&P 500 Index will best protect a portfolio

Accepted Answer

The S&P 500 Index is more like a portfolio that corresponds to the S&P 500 and thus is more protective of such a portfolio than of any of the other assets.

Question 4

If the hedge ratio for a stock call is 0.70, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

Call hedge ratio = N(d1); Put hedge ratio = N(d1) − 1; 0.7 − 1.0 = −0.3.

Question 5

Higher dividend-payout policies have a __________ impact on the value of the call and a __________ impact on the value of the put compared to lower dividend-payout policies.

Accepted Answer

Dividends lower the expected stock price, and thus lower the current call option value and increase the current put option value.

Question 6

If the hedge ratio for a stock call is 0.60, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

Call hedge ratio = N(d1); Put hedge ratio = N(d1) − 1; 0.6 − 1.0 = −0.4.

Question 7

A portfolio consists of 100 shares of stock and 1500 calls on that stock. If the hedge ratio for the call is 0.7, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

−$100 + [−$1,500(0.7)] = −$1,150.

Question 8

If the hedge ratio for a stock call is 0.50, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

Call hedge ratio = N(d1); Put hedge ratio = N(d1) − 1; 0.5 − 1.0 = −0.5.

Question 9

A $1 decrease in a call option's exercise price would result in a(n) __________ in the call option's value of __________ one dollar.

Accepted Answer

Option prices are less than stock prices, thus changes in stock prices (market or exercise) are greater (in absolute terms) than are changes in prices of options.

Question 10

Portfolio A consists of 600 shares of stock and 300 calls on that stock. Portfolio B consists of 685 shares of stock. The call delta is 0.3. Which portfolio has a higher dollar exposure to a change in stock price?

Accepted Answer

300 calls (0.3) = 90 shares + 600 shares = 690 shares; 685 shares = 685 shares.

Question 11

Lower dividend-payout policies have a __________ impact on the value of the call and a __________ impact on the value of the put compared to higher dividend-payout policies.

Accepted Answer

Dividends lower the expected stock price, and thus lower the current call option value and increase the current put option value.

Question 12

A put option is currently selling for $6 with an exercise price of $50. If the hedge ratio for the put is 0.30, and the stock is currently selling for $46, what is the elasticity of the put?

Accepted Answer

% stock price change = ($47 − $46)/$46 = 0.021739; % option price change = ($5.70 − $6.00)/$6 = − 0.05; − 0.05/0.021739 = − 2.30.

Question 13

Relative to European puts, otherwise identical American put options

Accepted Answer

It is valuable to exercise a put option early if the stock drops below a threshold price; thus American puts should sell for more than European puts.

Question 14

A portfolio consists of 400 shares of stock and 200 calls on that stock. If the hedge ratio for the call is 0.6, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

−$400 + [−$200(0.6)] = −$520.

Question 15

Portfolio A consists of 400 shares of stock and 400 calls on that stock. Portfolio B consists of 500 shares of stock. The call delta is 0.5. Which portfolio has a higher dollar exposure to a change in stock price?

Accepted Answer

400 calls (0.5) = 200 shares + 400 shares = 600 shares; 500 shares = 500 shares.

Question 16

Which one of the following variables influences the value of put options? I) Level of interest rates
II) Time to expiration of the option
III) Dividend yield of underlying stock
IV) Stock price volatility

Accepted Answer

All of the variables affect put option prices.

Question 17

An American call-option buyer on a nondividend-paying stock will

Accepted Answer

An American call-option buyer will not exercise early if the stock does not pay dividends; exercising forfeits the time value. Rather, the option buyer will sell the option to collect both the intrinsic value and the time value.

Question 18

Which one of the following variables influences the value of call options? I) Level of interest rates
II) Time to expiration of the option
III) Dividend yield of underlying stock
IV) Stock price volatility

Accepted Answer

All of the variables affect call option prices.

Question 19

A portfolio consists of 225 shares of stock and 300 calls on that stock. If the hedge ratio for the call is 0.4, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

−$225 + [−$300(0.4)] = −$345.

Question 20

Portfolio A consists of 500 shares of stock and 500 calls on that stock. Portfolio B consists of 800 shares of stock. The call delta is 0.6. Which portfolio has a higher dollar exposure to a change in stock price?

Accepted Answer

500 calls (0.6) = 300 shares + 500 shares = 800 shares; 800 shares = 800 shares.

Quiz 21: Option Valuation